A characterization of א1-free abelian groups and its application to the chase radical

Katsuya Eda

doi:10.1007/BF02766167

A characterization of א₁-free abelian groups and its application to the chase radical

Katsuya Eda^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

Abstract

A group A is an א₁-free abelian group iff A is a subgroup of the Boolean power Z^(B) for some complete Boolean algebra B. The Chase radical vA=Σ{C≦A: Hom(C, Z)=0 &C is countable). The torsion class {A:vA=A} is not closed under uncountable direct products.

Original language	English
Pages (from-to)	22-30
Number of pages	9
Journal	Israel Journal of Mathematics
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/BF02766167
Publication status	Published - 1987 Feb
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1007/BF02766167

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abstract = "A group A is an א1-free abelian group iff A is a subgroup of the Boolean power Z(B) for some complete Boolean algebra B. The Chase radical vA=Σ{C≦A: Hom(C, Z)=0 &C is countable). The torsion class {A:vA=A} is not closed under uncountable direct products.",

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AB - A group A is an א1-free abelian group iff A is a subgroup of the Boolean power Z(B) for some complete Boolean algebra B. The Chase radical vA=Σ{C≦A: Hom(C, Z)=0 &C is countable). The torsion class {A:vA=A} is not closed under uncountable direct products.

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A characterization of א₁-free abelian groups and its application to the chase radical

Abstract

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